\begin{frame}{Formulas with Free Variables} 
  \pause{} 
  \begin{block}{\ldots\ express properties and relations}
    \pause{}
    \begin{itemize}
      \item formula \alert{without} free variables: a \emph{sentence}
    \pause
      \item formula \alert{with one} free variable: an \emph{property}
    \pause
      \item formula \alert{with two or more} free variables: a \emph{relation}
    \end{itemize}
  \end{block}
  \pause

  \vspace*{-2ex}
  \begin{flushleft}
  \begin{minipage}{1.2\textwidth}
  $  
  \hspace*{-1.5em}
  \begin{array}{rll}  
   \formula{\unpred{L}{\const{r}}}  
     & \sentence{Roos is a logician} 
     & \pause{}\hspace*{-0.5ex}\text{(sentence)}
   \pause{}
   \\[0.5ex]
   \formula{\unpred{L}{\freevar{y}}}  
     & \sentence{$\freevar{y}$ is a logician} 
     & \pause{}\hspace*{-0.5ex}\text{(property)}
   \pause{}
   \\[0.5ex]
   \formula{\binpred{K}{\freevar{x}}{\freevar{y}}}  
     & \sentence{$\freevar{x}$ knows $\freevar{y}$} 
     & \pause{}\hspace*{-0.5ex}\text{(relation)} 
   \pause{}
   \\[0.5ex]
   \formula{\logand{\binpred{K}{\const{j}}{\const{r}}}
                   {\unpred{L}{\const{r}}}}  
     & \left\{\,\parbox{25ex}{\sentence{Jan knows Roos},\\[-0.25ex] \sentence{and Roos is a logician}}\right.
     & \pause{}\hspace*{-0.5ex}\text{(sentence)}
   \pause{}
   \\[1.75ex]
   \formula{\logand{\binpred{K}{\const{j}}{\freevar{y}}}
          {\unpred{L}{\freevar{y}}}}  
     & \sentence{Jan knows $\freevar{y}$, and $\freevar{y}$ is a logician} 
     & \pause{}\hspace*{-0.5ex}\text{(property)}
   \pause{}
   \\[0.5ex]
   \formula{\logand{\binpred{K}{\freevar{x}}{\freevar{y}}}
                   {\unpred{L}{\freevar{y}}}}  
     &  \sentence{$\freevar{x}$ knows $\freevar{y}$, and $\freevar{y}$ is a logician} 
     &  \pause{}\hspace*{-0.5ex}\text{(relation)} 
   \pause{}
   \\[0.5ex]
       % \eris x (Kjx \en Lx)    & &  \sentence{Jan kent een logicus} \\
   \formula{\existsst{x}{(\logand{\binpred{K}{\freevar{y}}{x}}{\unpred{L}{x}})}}
     &  \sentence{$\freevar{y}$ knows a logician} 
     & \pause{}\hspace*{-0.5ex}\text{(property)}
   \pause{}
   \\[0.5ex]
   \formula{\forallst{y}{\existsst{x}{(\logand{\binpred{K}{y}{x}}{\unpred{L}{x}}})}}
     & \sentence{Everybody knows a logician}
     & \pause{}\hspace*{-0.5ex}\text{(sentence)} 
  %\sentence{Iedereen  kent een domme logicus}  & &   \alle y \eris x (Kyx \en Lx \en Dx) 
  \end{array}
  $
  \end{minipage}
  \end{flushleft}
\end{frame}